Neoclassical Ion Flow Due to Inductive Electric Field in Tokamaks

Abstract

The influence of an inductive parallel electric field is usually neglected in the neoclassical transport theory for ions. In a recent paper, Catto et al. have claimed that the ion flow due to the inductive electric field is surprisingly large in the banana regime and it becomes comparable to the neoclassical ion flow driven by the ion temperature gradient. Their calculation relies on the use of the Kovrizhnikh and Hirshman–Sigmar model collision operators. The numerical factors for the expressions of ion flow velocities depend on the choice of model collision operators. Therefore, the following questions arise. How are their obtained numerical factors modified when we employ more accurate collision operator? Can we use the standard moment method of Hirshman for calculating the electric-field driven ion flow? The purpose of this short note is to answer these questions. A gyrophase averaged distribution function for species a is assumed to be slightly perturbed from the Maxwellian fa0 in an axisymmetric magnetic field B. Then, in the banana regime, the perturbed distribution function fa1 due to an inductive electric field E is identically zero for trapped particles and the perturbed distribution function for passing particles is obtained from hðB=vkÞ P b Cabð fa1; fb1Þi 1⁄4 ðea=TaÞhBEkifa0, where vk 1⁄4 v b and Ek 1⁄4 E b with b 1⁄4 B=B; ea and Ta are the charge and the temperature; and h i denotes a flux-surface average. The linearized Fokker-Planck collision operator for species a and b has the form Cabð fa1; fb1Þ Cabð fa1; fb0Þ þ Cabð fa0; fb1Þ, where Cabð fa1; fb0Þ and Cabð fa0; fb1Þ represent the Landau collision operators for the perturbed test and field particle distributions. We here use the following approximation for the collision operator Cabð fa1; fb1Þ 1⁄4 DabðvÞLð fa1Þ þ C abð f 1 a1; f 1 b1Þ þ D abðvÞf 1 a1 ; ð1Þ